Based on the description on their site, the controller includes a built-in battery: "8.39 Wh Li-ion battery, 35+ hours of gameplay... "
That was disappointing for me. Specially condidering the Steam Frame's controllers make use of AA batteries: "One replaceable AA battery per controller, 40hr battery life"
AA Batteries might not be as convenient to use, but being able to replace them is a great advantage. All my Xbox360 controllers still work fine, but none of my PS3' Dualshock 3s.
The official docking station could be used to recharge (rechargables) AA batteries so the functionality could remain the same.
Let's compare against msrp please.
Why? The price you're actually going to pay is what matters. Though even if you insist on MSRP for some reason, the DualSense is $75 and the Xbox controller is $65, and you can get these for $25 MSRP ($18 actual) for two, making the Xbox controller barely more expensive if you have an even number of them.
If you compare the prices today, the Xbox controller is $50 compared to its $65 MSRP and the DualSense is $74 with a $75 MSRP, so you can get two battery packs and a controller and still pay $68, $6 less.